Topic: Networks, Signals and Systems
Given a real sequence and 8 point DFT output are $X(0)=5, X(1)=1+j, X(2)=3+j, X(3)=2+3j$. What is $X(6)$?
- A. 2-3j
- B. 3-j
- C. 1-j
- D. 1+j
Answer: B. 3-j
Explanation: The N-point Discrete Fourier Transform (DFT) of a real-valued sequence exhibits conjugate symmetry, which is expressed as $X(N-k) = X^*(k)$. Here, $N = 8$. To find $X(6)$, we use the symmetry property: $X(6) = X(8-2) = X^*(2)$. Given $X(2) = 3+j$, its complex conjugate is $3-j$.